In 1940, the Bolshoi Theatre in Moscow invited the Russian film director Sergei Eisenstein to stage Richard Wagner's Die Walküre. He eagerly accepted the new challenge, as it presented him with an opportunity to apply Wagner's ideas of combining theatre, music, literature and myth in one medium, which concurred with his own vision of film as synthesis.

Eisenstein wanted "The Ride of the Valkyries" to "envelop the entire audience via a system of loudspeakers reverberating as if in flight from the rear of the stage to the back of the auditorium and back. And roll around the auditorium, up the steps and along the aisles and corridors. But I was not able to overcome the traditions of the opera theatre!" Eisenstein was anticipating "The Ride of the Valkyries" as used in the stereophonic Dolby system by Francis Ford Coppola in Apocalypse Now (the background to American helicopters bombing the hell out of the Vietcong) almost four decades later.

According to the American director and screenwriter Harmony Korine: "If Wagner lived today, he would probably work with film instead of music. He already knew back then that the Great Art Form would include a sort of fourth dimension; it was really film he was talking about."

It could be argued that if film resembles any other art form, it is closer to opera than theatre or literature; of the operatic composers, Wagner could lay claim to being the most "cinematic". For example, in the Festspielhaus in Bayreuth, the theatre built by Wagner specifically to present Der Ring des Nibelungen, a hidden orchestra was conceived so that the music could be heard like a soundtrack. Wagner also had all the house lights turned off, unusually for the 1870s. In addition, an illusion was created by a dual proscenium which, according to Wagner, "allows the performers to appear enlarged and on a superhuman scale" - the theatrical equivalent of the close-up.

A multitude of film scores rely on Wagnerian leitmotifs - a musical phrase, associated with some particular character or idea - and the edited flow of images could be likened to Wagner's "continuous melody". More comparisons could be made between Wagner and film, and there have been learned treatises on the influence of Wagner on movies from Fritz Lang's early epics, Die Nibelungen and The Testament of Dr Mabuse, to Star Wars and The Lord of the Rings. However, though bleeding chunks of his music have been heard in hundreds of movies, particularly the over(mis)used "The Ride of the Valkyries", the composer has been rather ill-served by the cinema. But, as Mark Twain once quipped, "Wagner's music is better than it sounds." In films, at least.

In 1960, Luis Buñuel added a musical soundtrack to his silent surrealist masterpiece, Un Chien Andalou (1928), including the mystically rapturous "Liebestod" from Tristan und Isolde. He used it again, even more brilliantly, in L'Age d'Or (1930) as accompaniment to a woman performing fellatio on the white toe of a marble statue and to a couple in the throes of "l'amour fou".

Preston Sturges's Unfaithfully Yours has a famous conductor (Rex Harrison) imagining, while conducting three different works, three different ways of taking revenge on his wife, whom he suspects of infidelity. The nature of his imaginings is dictated by that of the music: during Wagner's reconciliation theme from Tannhäuser, he fantasises about forgiving his wife and allowing her to run off with her young lover.

Naturally, Hollywood, always deeply suspicious of "high art", would mostly caricature Wagner's work. Whenever there is an opera scene in the movies, it's more than likely to show a giantess wearing a horned Viking helmet and belting out Wagner at the top of her lungs. In What's New, Pussycat?, Peter Sellers as the crazy psychiatrist Fritz Fassbender has to cope with "the wife that ate Europe", who is depicted as the stereotypical Wagnerian soprano.

As Hollywood musicals have been an antidote to solemnity, classical music could only be swallowed if the pill was sugared. This has led to some weird incongruities, such as the famed Norwegian dramatic soprano Kirsten Flagstad being introduced by Bob Hope in The Big Broadcast of 1938, and then superbly delivering Brunhilde's battle cry from Die Walküre. No wonder audiences were confused and didn't know whether or not to laugh. Lauritz Melchior, the great Danish Wagnerian heldentenor, brought a bit of culture, sturdy singing and good nature to his appearances in five Hollywood musicals, appearing opposite the likes of glamorous swimming star Esther Williams (in lieu of a Rhine maiden) and singing the "Prize Song" from Die Meistersinger for the delight of June Allyson and Kathryn Grayson in Two Sisters From Boston (1946). The most bizarre rendering of the "Prize Song" has to be by the Andy Warhol hunk Joe Dallesandro in Louis Malle's Black Moon, 1974.

The apotheosis of Wagner in American movies came with Chuck Jones's animated short What's Opera, Doc? featuring Elmer Fudd as Siegfried in hapless pursuit of Bugs Bunny. "Kill the wabbit!" sings Elmer, until he sets eyes on the beautiful Bugs in drag as Brunhilde. They sing a love duet. "Oh, Bwunhilda, you're so wuvwee." "O mighty warrior of great fighting stock. Might I inquire to ask, eh, what's up Doc?" The film underlined the already prevalent cartoonish view of the composer.

Wagner's life has been treated in a serious manner on film, however, despite some unintentional laughs. The first biopic, Carl Froelich's The Life of Richard Wagner, appeared as early as 1913. One of the true rarities in the Wagner on Screen season at the BFI, it starred Italian composer Giuseppe Becce, who also scored the music.

In the major biopics, for some reason, this most German of composers has been portrayed by some of the most British of actors: Alan Badel, Richard Burton and Trevor Howard. Badel played him as a bored sybarite in the kitsch Magic Fire, in which the music was "arranged" by Erich Wolfgang Korngold, who managed to reduce the Ring Cycle to four minutes, and who decided to appear in the film as the conductor Hans Richter "to protect Wagner", as he claimed. Both Howard and Burton (in Luchino Visconti's Ludwig, 1972, and Tony Palmer's 300-minute Wagner, 1983) played the composer as a petulant genius.

The terribly English Lyndon Brook was Wagner to Dirk Bogarde's unlikely Franz Liszt in Song Without End (1960). No less convincing were pop singers Paul Nicholas (Wagner) and Roger Daltrey (Liszt) in Ken Russell's fanciful Lisztomania (1976).

In Ludwig: Requiem for a Virgin King (1972), Wagner is played by both a woman and a dwarf. Hans-Jürgen Syberberg's collage of German history, culture and psychology - revealing the inner and outer life, real or imagined, of Wagner's great patron, the mad castle-building King of Bavaria - says far more about Ludwig (and Wagner) than Visconti's sumptuous soap opera.

It was inevitable that Syberberg, the chronicler of the German soul, should tackle Wagner's last opera, the synthesis of the composer's own religious and mystic beliefs. While demystifying Wagner's work, Parsifal (1982) also presents it as an unassailable masterpiece. The action takes place on and around a gigantic death mask of Wagner, and embraces a wide range of startling images, associations and techniques - long takes, back projection, puppets and tableaux vivants. The most daring device has Parsifal played both by a boy, who represents the "fool", and a girl, an asexual symbol of purity whom he becomes after Kundry's kiss. This splendidly sung and acted celebration is the most personal and imaginative of opera films. Whether Wagner would have approved is another matter.

What the films in the BFI season reveal is that, unlike the more monomorphic view of, say, Beethoven or Verdi, Wagner - the most revered, reviled, complex and misunderstood of composers - is many different things to many different people.